Câu hỏi của Giang Vân Nhi Anh

Question

Chứng minh

a, A = $\dfrac{1}{5}$ + $\dfrac{1}{6}$ + $\dfrac{1}{7}$ + ... + \(...

Nguyễn Thanh Hằng · Accepted Answer

a, Ta có :

$\dfrac{1}{6}< \dfrac{1}{5}$

$\dfrac{1}{7}< \dfrac{1}{5}$

.................

$\dfrac{1}{9}< \dfrac{1}{5}$

$\dfrac{1}{10}=\dfrac{1}{10}$

$\dfrac{1}{11}< \dfrac{1}{10}$

..................

$\dfrac{1}{17}< \dfrac{1}{10}$

$\Leftrightarrow\dfrac{1}{5}+\dfrac{1}{6}+\dfrac{1}{7}+......+\dfrac{1}{17}< \dfrac{1}{5}+\dfrac{1}{5}+....+\dfrac{1}{5}$

$\Leftrightarrow A< \dfrac{1}{5}.5+\dfrac{1}{10}.8$

$\Leftrightarrow A< 1+\dfrac{4}{5}=\dfrac{9}{5}< 2$

$\Leftrightarrow A< 2\left(đpcm\right)$

b/ Ta có :

$\dfrac{1}{11}>\dfrac{1}{30}$

$\dfrac{1}{12}>\dfrac{1}{30}$

...............

$\dfrac{1}{29}>\dfrac{1}{30}$

$\dfrac{1}{30}=\dfrac{1}{30}$

$\Leftrightarrow\dfrac{1}{11}+\dfrac{1}{12}+........+\dfrac{1}{30}>\dfrac{1}{30}+\dfrac{1}{30}+.......+\dfrac{1}{30}$

$\Leftrightarrow B>\dfrac{1}{30}.20=\dfrac{2}{3}$

$\Leftrightarrow B>\dfrac{2}{3}\left(đpcm\right)$

Câu trả lời: